This work presents an approach to the abstract mathematical analysis of the evolution of a species. A mathematical model is proposed as well that characterizes the natural evolution phenomena of a species. On the basis of this model, the convergence of a new computational evolutionary algorithm is developed and proven, that is applied to minimizing (or maximizing) a costs function that meets certain requirements. Simulation studies are carried out in order to validate the theoretical aspects and to evaluate the performance of the evolutionary algorithm. ©2006 IEEE.